A Hopf bifurcation theorem for singular differential–algebraic equations

R. Beardmore and K. Webster

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1383-1395

Abstract: We prove a Hopf bifurcation result for singular differential–algebraic equations (DAE) under the assumption that a trivial locus of equilibria is situated on the singularity as the bifurcation occurs. The structure that we need to obtain this result is that the linearisation of the DAE has a particular index-2 Kronecker normal form, which is said to be simple index-2. This is so-named because the nilpotent mapping used to define the Kronecker index of the pencil has the smallest possible non-trivial rank, namely one. This allows us to recast the equation in terms of a singular normal form to which a local centre-manifold reduction and, subsequently, the Hopf bifurcation theorem applies.

Keywords: Hopf bifurcation; Singularity; Differential–algebraic equations (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1383-1395

DOI: 10.1016/j.matcom.2008.03.009

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